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|a (JST)3448537
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|b ger
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|a eng
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|a 62F15
|2 MSC
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|a 62C10
|2 MSC
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|a Abraham, Christophe
|e verfasserin
|4 aut
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|a Asymptotic Global Robustness in Bayesian Decision Theory
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|c 2004
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|a Text
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|a In Bayesian decision theory, it is known that robustness with respect to the loss and the prior can be improved by adding new observations. In this article we study the rate of robustness improvement with respect to the number of observations n. Three usual measures of posterior global robustness are considered: the (range of the) Bayes actions set derived from a class of loss functions, the maximum regret of using a particular loss when the subjective loss belongs to a given class and the range of the posterior expected loss when the loss function ranges over a class. We show that the rate of convergence of the first measure of robustness is √n, while it is n for the other measures under reasonable assumptions on the class of loss functions. We begin with the study of two particular cases to illustrate our results.
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|a Copyright 2004 Institute of Mathematical Statistics
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|a Bayesian Decision Theory
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|a Asymptotic Robustness
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|a Class of Loss Functions
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|a Behavioral sciences
|x Psychology
|x Cognitive psychology
|x Cognitive processes
|x Decision making
|x Bayesian theories
|x Bayes estimators
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|a Mathematics
|x Mathematical analysis
|x Mathematical robustness
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|a Mathematics
|x Mathematical expressions
|x Mathematical functions
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|a Information science
|x Information analysis
|x Data analysis
|x Bayesian analysis
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|a Mathematics
|x Mathematical procedures
|x Approximation
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|a Behavioral sciences
|x Psychology
|x Cognitive psychology
|x Decision theory
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|a Mathematics
|x Pure mathematics
|x Probability theory
|x Random variables
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|a Physical sciences
|x Physics
|x Mechanics
|x Density
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|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Statistical distributions
|x Distribution functions
|x Probability distributions
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|a Mathematics
|x Mathematical values
|x Mathematical variables
|x Mathematical independent variables
|x Robustness
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|a research-article
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|a Cadre, Benoît
|e verfasserin
|4 aut
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|i Enthalten in
|t The Annals of Statistics
|d Institute of Mathematical Statistics
|g 32(2004), 4, Seite 1341-1366
|w (DE-627)270129162
|w (DE-600)1476670-X
|x 00905364
|7 nnns
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|g volume:32
|g year:2004
|g number:4
|g pages:1341-1366
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|u https://www.jstor.org/stable/3448537
|3 Volltext
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|d 32
|j 2004
|e 4
|h 1341-1366
|